Game Theory Applications:
Lecture Notes
Course Website
http://www.citi.umich.edu/u/galka/games
 Galina Albert Schwartz
 Department of Finance
 University of Michigan
 Business School
04.16.01 and 04.18.01
Lecture Notes in Game Theory
1
Summary of last two
lectures
Auctions: Dixit, chapter 15
 Types of Auctions
 Winner’s Curse
 Vickrey’s Theorem
 Auction Design
 Summary of the Course

04.16.01 and 04.18.01
Lecture Notes in Game Theory
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Auction Design:
Types of Auctions
 Four
Major Considerations
– Types of Auction Settings
– Bidding Types
– Pricing Schemes
– Valuation Methods
04.16.01 and 04.18.01
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Types of Auction Settings
 English
Auction
– history: used by major auction houses,
Cristie’s and Sotheby’s
– Major Feature: Ascending Price
 Dutch
Auction
– history: used in tulip trading
– Major Feature: Descending Price
04.16.01 and 04.18.01
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Bidding Types
– Sealed bid auction
»Advantage: makes collision more
difficult
– Open-outcry auction
»advantage: casts additional
information to the bidders about the
object value
04.16.01 and 04.18.01
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Valuation Methods
 Two
major methods [types of objects]
– private (subjective valuation)
» different bidders value the object differently
» example: collectibles
– common (public, objective value)
» All bidders have the same value, [but might have
different estimates of this value]
» example: oil fields
04.16.01 and 04.18.01
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Pricing Schemes
 First
Price Auction
– no true price revelation
– price is shaded (lower than the true
value)
 Second
Price Auction
– price is revealed truthfully under
`reasonable` conditions
– [proven by Vickrey (1996 Nobel Price)]
04.16.01 and 04.18.01
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Winner’s Curse
 When
the Winner’s Curse is a
problem
– common value auctions
– high level of uncertainty of the object
value
 How
to alleviate the Winner’s Curse
– Use Second Price Auction
04.16.01 and 04.18.01
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Revenue Equivalence Theorem
 `reasonable`
conditions are:
– bidders are risk-neutral
– object is of a common value
– bidder’s estimates of this value are
independent ==>

Revenue Equivalence Theorem holds:
All types of auctions on average yield the
same outcome (i.e. the same profit [surplus])
04.16.01 and 04.18.01
Lecture Notes in Game Theory
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Departures from the Theorem’s
Conditions & Auction Design

Assume that bidders are risk-averse
& object is of a common value &
bidder’s estimates of this value are
independent
– Then
04.16.01 and 04.18.01
Lecture Notes in Game Theory
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Departures from the Theorem’s
Conditions & Auction Design
 Assume
that bidders are risk-neutral
& their valuation estimates are
positively correlated
– Then
04.16.01 and 04.18.01
Lecture Notes in Game Theory
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All-Pay Auctions

All bidders pay their bids, but only
one [or several] get the object
– example: athletic competitions
 Optimal
bidding strategy in all-pay
auctions:
Use of Mixed strategy
04.16.01 and 04.18.01
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Some Other
Considerations
Reserve Price of the object
 Information disclosure
 Why e-Bay is a second price auction
 Auctions and Stock market: are
there any similarities?
 Auctions and LBOs: are there any
similarities?

04.16.01 and 04.18.01
Lecture Notes in Game Theory
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Government Objective Function
 Duality
of Government Objective
– to maximize the auction revenues
– to maximize the government revenues that auction
brings [auction revenue & future tax revenues from
the corporations who submitted the winning bids]
– to maximize economic efficiency of provision of the
goods related to auction in question
– to maximize the total surplus of the specific
auction [a sum of government revenues [seller’s
surplus], corporate profits [buyer’s or bidder’s
surplus], and consumer surplus
04.16.01 and 04.18.01
Lecture Notes in Game Theory
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Can Everyone be a Winner?
 Example
of California Energy Crisis
– I promise a 6 times drop in the price of
electricity in CA [three years ago]
– why the academicians are silent?
 Example
of British Government
Auction Policy
– Klemperer [Oxford] designed the
system for the Government [ seller]
– he also consults the companies [bidders]
04.16.01 and 04.18.01
Lecture Notes in Game Theory
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Summary of Auctions I
 auctions
can be
» English (ascending) & Dutch (descending)
» open outcry & sealed bid
» first price & second price
» common value & private value
 Auction
Theory major results
» Revenue Equivalence Theorem
» Vickrey’s mechanism (truthful price
revelation via second-price sealed bid
auction)
04.16.01 and 04.18.01
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Summary of Auctions II
 What
matters for auction design
– bidder’s (buyer’s) features:
» risk attitude (risk-neutral or risk-averse)
» their valuation of the object(independent or
correlated)
– Seller’s objective function
» short-term surplus maximization
» long -term considerations
» economic efficiency (government is a seller)
– Information Structure
04.16.01 and 04.18.01
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Summary of the Course
 We
learned:
– Dixit, chapters: 1 – 5, 15, 16 + some
extras
– Lewis, chapters: ALL (the entire book)
 Major Lesson from our studies:
– common sense works
– `common` theory works better, because it
» aggregates the common sense,
» structures it, and
» makes it from the art into a science
04.16.01 and 04.18.01
Lecture Notes in Game Theory
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